One can also consider embeddings of charts \(\Phi :(R,U,f,i)\hookrightarrow (S,V,g,j)\)  for \(R\rightarrow S\rightarrow X\)  étale maps, i.e. a locally closed embedding \(\Phi :U\rightarrow V\)  such that \(\Phi \circ i=j|_R:R\rightarrow V\)  and \(f=g\circ \Phi :U\rightarrow \mathbb {C}\) . According to [1]}, one can compare two critical charts using embeddings: namely, for \((R,U,f,i)\)  and \((S,V,g,j)\)  two critical charts and \(x\in R\cap S\) , there exist subcharts \((R^{\prime },U^{\prime },f^{\prime },i^{\prime })\subset (R,U,f,i)\)  and \((S^{\prime },V^{\prime },g^{\prime },j^{\prime })\subset (S,V,g,j)\)  such that \(x\in R^{\prime }\cap S^{\prime }\) , a critical chart \((T,W,h,k)\)  and embeddings \(\Phi :(R^{\prime },U^{\prime },f^{\prime },i^{\prime })\hookrightarrow (T,W,h,k)\)  and \(\Psi (S^{\prime },V^{\prime },g^{\prime },j^{\prime })\hookrightarrow (T,W,h,k)\) .
